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This thesis contributes a novel receptance coupling technique to analyse dynamic response localization induced by bandgap mechanisms in advanced periodic light weight material and structural systems. One-dimensional structural systems are used to illustrate the technique with experiments. Localization induced by disorder and nonlinearity is investigated using numerical simulations. Insights on bandgap localization mechanisms offered by the receptance technique can be used to design periodic composite materials such as Phononic Crystals and metamaterials, and periodic structures with enhanced vibroacoustic performance characteristics.

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